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arXiv · 1401.6238

Fast Hankel Tensor-Vector Products and Application to Exponential Data Fitting

Weiyang Ding·Liqun Qi·Yimin Wei
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Abstract

This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{anti-circulant} tensors. Then we obtain a fast algorithm for Hankel tensor-vector products by embedding a Hankel tensor into a larger anti-circulant tensor. The computational complexity is about $\mathcal{O}(m^2 n \log mn)$ for a square Hankel tensor of order $m$ and dimension $n$, and the numerical examples also show the efficiency of this scheme. Moreover, the block version for multi-level block Hankel tensors is discussed as well. Finally, we apply the fast algorithm to exponential data fitting and the block version to 2D exponential data fitting for higher performance.

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Weiyang Ding, Liqun Qi, Yimin Wei. 2014-01-24. Fast Hankel Tensor-Vector Products and Application to Exponential Data Fitting. https://arxiv.org/abs/1401.6238

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